Question

6x−y=−14
2x−3y=6

Solve it in elimination method

Answer 1

• 
  `x = - 3`
• 
  `y = - 4`

Explanation:

The given equations to us are ,

1. 6x - y = -14
2. 2x - 3y = 6

In elimination method we eliminate any variable and then find the find the value of second unknown variable. Using that value we can find the value of 1st variable.

Multiply equation 1 by 3 ,

3(6x-y)=-14*3

18x - 3y = -42 ..... (3)

Now subtract equation 2 and 3 to eliminate y as,

2x - 3y - (18x -3y) = 6 -(-42)

2x -3y -18x +3y = 6+42

-16x = 48

x = 48/-16 = -48/16

x = -3

Substitute this value in equation 2 ,

2*(-3) -3y = 6

-6-3y =6

-3y =6+6

-3y = 12

y = -4

And we are done!

Answer 2

x = -3

y = -4

Explanation:

Given system of equations:

`\begin{cases}6x-y=-14\\2x-3y=6\end{cases}`

Multiply the second equation by -3:

`\implies 2x(-3)-3y(-3)=6(-3)`

`\implies -6x+9y=-18`

Add this to the first equation to eliminate the term in x:

`\begin{array}{crcrcl}\vphantom{\frac12}& 6x & - & y & = & -14\\\vphantom{\frac12}+ & (-6x & + & 9y & = & -18)\\\cline{2-6}\vphantom{\frac12}&&&8y&=&-32\\\cline{2-6}\end{array}`

Solve the equation for y:

`\implies 8y=-32`

`\implies y=-4`

Substitute the found value of y into one of the original equations and solve for x:

`\implies 2x-3(-4)=6`

`\implies 2x+12=6`

`\implies 2x=-6`

`\implies x=-3`

Therefore, the solution to the given system of equations is (-3, -4).